Sunday, September 22, 2013

The Importance of Number Lines

Do you use a number line in your classroom?
If you're like most, you've probably said the phrase "use your number line"  to students struggling with math at least a few times day day!

But the number line is SO much more than a simple tool to help students count forward or backward! Numberlines and horizontal thinking are mentioned throughout the Common Core State Standards.  Thinking horizontally is probably more important than any of us ever thought! Today, I'd like  to show you a few examples of what you can do on a number line and in turn stress how important it is to use number lines in early education!
First, let's get a definition straight. This is called an open number line.
 You'll notice two arrows on each side, demonstrating that numbers continue in both directions forever. You'll also notice that this number line doesn't have any numbers.... yet!!

 Number Line Warm Up
Let's start with a great math lesson warm up- draw three numbers out of the bag, and place them on the number line. How close should the numbers be? How far apart? Are two of the numbers
closer than the other? Next, place a "?" on the number line. What number might be represented by the "?"

Addition Samples
Addition is another wonderful way to think about the number line. Start at any given number and add logical pieces of the second addend until you arrive at the sum.  Let's try 127+ 213.
I started with 127. Since I'm only 3 numbers away form 130, I decided to add three ones next.  From there, I counted two groups of 100 and a group of ten. The sum is 340.

I could have broken up the "chunks" of 213 in a variety of ways. I might have also decided to start with the largest added, 213, and add 127. The beauty in this is that there isn't one set way of using a number line, so students are free to solve the problem in any way that makes sense to them!

Subtraction Samples
Can I subtract on a number line too? Let's check it out and try 340- 127.
 Since my number will get smaller, I'll start with the largest number and place it on the right of my number line. I can subtract any number, any amount of numbers, so long as it equals 127.  I've chosen to subtract according to place value, so I'll subtract a group of 100, two groups of 10, and 7.  Again, there are multiple ways you might choose to subtract- there's no single path to the difference!


Multiplication Samples
The number line is great for representing groups.  We'll start with an easy one,  3x5 ( three groups of 5). Here, you can see that I'm creating three groups, with five in each group, by "jumping" the number line in groups of 5, for a total of 15.
This works no matter how high the numbers! What would 17x25 look like? 17 groups of 25 would take too long, so I decided to chunk in groups of 4. Since 4 groups of 25 make 100, I'll show four groups of 100- this makes 400, or 16x25. Since the problem asks for 17x25, I'll add one more group of 25, for a total of 425. Again there are multiple ways of arriving at 425, and I encourage you and your students to create multiple ways to solve the same problem!

Division Samples
Yes Virginia, there is a way to divide on the number line! How many groups of 25 are in 425?


I start with the total, 425. If I take away 4 groups of 25 (100), then I'm at 325. I'll take out three more groups of 100 ( 4 groups of 25), which gets me to 25. If I take out one more group of 25, then I've arrived at 0. This tells me there are no remainders. How many times did I take away 25? A total of 17, so 425 divided by 25 must equal 17.


Our number line fun doesn't have to end here. Number lines will play an important role in fourth grade fraction studies as well. I'd like to encourage ALL elementary, starting with Kindergarten, to incorporate a number line into your "toolbox of strategies." If students understand how to manipulate number lines in early elementary, they're more likely succeed in higher elementary math with number line strategies as well.

So what's next?
Check out some of my favorite number line resources to use in your classrooms!



Number Line Freebie Resource- click here!





Number Line Nightmare-  a fun Halloween themed activity where students Gr.k-2 use a number line to order various pumpkin numbers- click here!






           Number Line Math Meetings and Center Activities grades K-1

   The number line is one of the most beneficial daily exercises you can add to your morning meeting. This one simple tool assists your students in building a strong foundation in number sense!
    Use this tool 5 minutes a day during your morning meeting to increase your students' number sense! Activities and cards focus on numbers 0-20.
 Click here to get yours!

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